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Analysis with an Introduction to Proof [Print Replica]
Author(s): Steven Lay (Author), Richard Ligo (Author)
- Publisher Finelybook 出版社: Pearson
- Publication Date 出版日期: August 28, 2024
- Edition 版本: 6th
- Language 语言: English
- ASIN: B0FF9XD5YP
- ISBN-13: 9780135393925
Book Description
Analysis with an Introduction to Proofeases your transition to advanced mathematics, building the foundation that is essential to help you succeed in real analysis (often considered the most difficult course in the undergrad math curriculum). It introduces logic and emphasizes the structure and nature of the arguments used, helping you move from earlier, computationally oriented courses to working with proofs. Helpful examples and practice problems, numerous drawings, and selected hints/answers make the material both readable and user friendly.
The 6th Editionwelcomes new co-author Richard Ligo, adds new GeoGebra-powered Interactive Figures, expands on the text’s hallmark strengths, and more.
Table of Contents
Copyright Page
Pearson’s Commitment to Accessibility
Contents
Dedication
Preface
Chapter 1 Logic and Proof
Section 1.1 Logical Connectives
Section 1.2 Quantifiers
Section 1.3 Techniques of Proof: I
Section 1.4 Techniques of Proof: II
Chapter 2 Sets and Functions
Section 2.1 Basic Set Operations
Section 2.2 Relations
Section 2.3 Functions
Section 2.4 Cardinality
Section 2.5 Axioms for Set Theory
Chapter 3 The Real Numbers
Section 3.1 Natural Numbers and Induction
Section 3.2 Ordered Fields
Section 3.3 The Completeness Axiom
Section 3.4 Topology of the Real Numbers
Section 3.5 Compact Sets
Section 3.6 Metric Spaces
Chapter 4 Sequences
Section 4.1 Convergence
Section 4.2 Limit Theorems
Section 4.3 Monotone Sequences and Cauchy Sequences
Section 4.4 Subsequences
Chapter 5 Limits and Continuity
Section 5.1 Limits of Functions
Section 5.2 Continuous Functions
Section 5.3 Properties of Continuous Functions
Section 5.4 Uniform Continuity
Section 5.5 Continuity in Metric Spaces
Chapter 6 Differentiation
Section 6.1 The Derivative
Section 6.2 The Mean Value Theorem
Section 6.3 L’Hospital’s Rule
Section 6.4 Taylor’s Theorem
Chapter 7 Integration
Section 7.1 The Riemann Integral
Section 7.2 Properties of the Riemann Integral
Section 7.3 The Fundamental Theorem of Calculus
Chapter 8 Infinite Series
Section 8.1 Convergence of Infinite Series
Section 8.2 Convergence Tests
Section 8.3 Power Series
Chapter 9 Sequences and Series of Functions
Section 9.1 Pointwise and Uniform Convergence
Section 9.2 Applications of Uniform Convergence
Section 9.3 Uniform Convergence of Power Series
Glossary of Key Terms
References
Hints for Selected Exercises
Index
